MATH214-Final-Project
Ahmed A. Radhi - 100049714
Khalid Talal Suliman - 100053835
5/7/2021
# Loading Libraries
library(tidyverse)## -- Attaching packages --------------------------------------- tidyverse 1.3.0 --## v ggplot2 3.3.3 v purrr 0.3.4
## v tibble 3.1.0 v dplyr 1.0.5
## v tidyr 1.1.3 v stringr 1.4.0
## v readr 1.4.0 v forcats 0.5.1## Warning: package 'tidyr' was built under R version 4.0.5## Warning: package 'dplyr' was built under R version 4.0.5## Warning: package 'stringr' was built under R version 4.0.5## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()library(magrittr)##
## Attaching package: 'magrittr'## The following object is masked from 'package:purrr':
##
## set_names## The following object is masked from 'package:tidyr':
##
## extractlibrary(modelr)
library(nycflights13)
library(lubridate)##
## Attaching package: 'lubridate'## The following objects are masked from 'package:base':
##
## date, intersect, setdiff, unionlibrary(splines)
library(forcats)
library(plotly)## Warning: package 'plotly' was built under R version 4.0.5##
## Attaching package: 'plotly'## The following object is masked from 'package:ggplot2':
##
## last_plot## The following object is masked from 'package:stats':
##
## filter## The following object is masked from 'package:graphics':
##
## layoutIntroduction and Description
The data is provided by data.gov.uk. It describes road accidents across Leeds in the year 2017. Between all datasets, this dataset was selected because it includes around 2,200 accident with 15 variable that can be easily parsed and explored. Also, we selected this dataset because we believe that there are different questions that can be asked about the data, and that the data can provide interesting answers for our questions. The dataset includes data such as location, date, time, road setting and casualty information for each accident that transpired during the year.
Reference : https://data.world/datagov-uk/6efe5505-941f-45bf-b576-4c1e09b579a1
Data Parsing and Import
# Loading & Parsing Data
Accidents_2017 <- read_csv("Data/datagov-uk-6efe5505-941f-45bf-b576-4c1e09b579a1/2017-8.csv",
col_names = c("Reference_Number","Easting","Northing","Vehicles_Num","Accident_Date","Time","Road_Class","Road_Surface",
"Lightning_Cond","Weather_Cond","Vehicle_Type","Casualty_Class","Severity","Gender","Age"), skip = 1)##
## -- Column specification --------------------------------------------------------
## cols(
## Reference_Number = col_character(),
## Easting = col_double(),
## Northing = col_double(),
## Vehicles_Num = col_double(),
## Accident_Date = col_character(),
## Time = col_character(),
## Road_Class = col_character(),
## Road_Surface = col_character(),
## Lightning_Cond = col_character(),
## Weather_Cond = col_character(),
## Vehicle_Type = col_character(),
## Casualty_Class = col_character(),
## Severity = col_character(),
## Gender = col_character(),
## Age = col_double()
## )Accidents_Date <- Accidents_2017$Accident_Date
Accidents_Date <- parse_date(Accidents_Date, "%m/%d/%Y")
Time <- Accidents_2017$Time
Time <- parse_time(Time, "%H%M")
Accidents_2017 <- Accidents_2017 %>%
select(1:4, 7:15) %>%
mutate(Accidents_Date, Time)
Accidents_2017 <- Accidents_2017[,c(1:4,14,15,5:13)]
# Correcting spelling mistakes
Lightning_Cond <-
str_replace(Accidents_2017$Lightning_Cond,"Darkness: Street lights present and lit and lit","Darkness: Street lights present and lit")
Road_Class <- str_replace_all(Accidents_2017$Road_Class,
c("A.*" = "A","B.*" = "B","M.*" = "M"))
Road_Surface <- str_replace(Accidents_2017$Road_Surface,"^F.*","Snow")
Weather_Cond <- word(Accidents_2017$Weather_Cond,1)
Weather_Cond <- str_replace(Weather_Cond,"Fog","Other")
Vehicle_Type <- word(Accidents_2017$Vehicle_Type,1)
Vehicle_Type <- str_replace_all(Vehicle_Type,
c(".Private" = "Taxi",
"Ca.*" = "Car","Pedal" = "Cycle"))
Vehicle_Type <- str_replace(Vehicle_Type,"TaxiTaxi", "Taxi")
# Adding the improved columns to the dataset
Accidents_2017 <- Accidents_2017 %>%
select(1:6,12:15) %>%
mutate(Lightning_Cond,Weather_Cond,Road_Class,Road_Surface,Vehicle_Type,
Year = year(Accidents_Date),
Month = month(Accidents_Date),
Day = day(Accidents_Date),
Hour = hour(Time),
Minute = minute(Time),
Accidents_DateTime = make_datetime(Year, Month, Day, Hour, Minute))
Accidents_2017 <- Accidents_2017[,c(1:4, 16:20, 5:6, 21, 7:15)]
# Assigning the columns to their proper classes.
for(i in 2:length(Accidents_2017)) {
if(is.character(Accidents_2017[[i]])) {
Accidents_2017[[i]] <- as.factor(Accidents_2017[[i]])
} else if (is.numeric(Accidents_2017[[i]])) {
Accidents_2017[[i]] <- as.numeric(Accidents_2017[[i]])
}
}
map(Accidents_2017,class)## $Reference_Number
## [1] "character"
##
## $Easting
## [1] "numeric"
##
## $Northing
## [1] "numeric"
##
## $Vehicles_Num
## [1] "numeric"
##
## $Year
## [1] "numeric"
##
## $Month
## [1] "numeric"
##
## $Day
## [1] "numeric"
##
## $Hour
## [1] "numeric"
##
## $Minute
## [1] "numeric"
##
## $Accidents_Date
## [1] "Date"
##
## $Time
## [1] "hms" "difftime"
##
## $Accidents_DateTime
## [1] "POSIXct" "POSIXt"
##
## $Casualty_Class
## [1] "factor"
##
## $Severity
## [1] "factor"
##
## $Gender
## [1] "factor"
##
## $Age
## [1] "numeric"
##
## $Lightning_Cond
## [1] "factor"
##
## $Weather_Cond
## [1] "factor"
##
## $Road_Class
## [1] "factor"
##
## $Road_Surface
## [1] "factor"
##
## $Vehicle_Type
## [1] "factor"Accidents_2017## # A tibble: 2,203 x 21
## Reference_Number Easting Northing Vehicles_Num Year Month Day Hour Minute
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 3AP0313 426340 428455 1 2017 3 17 8 15
## 2 3BE0850 430828 433222 2 2017 1 14 13 30
## 3 4110858 428940 429856 2 2017 1 1 8 5
## 4 4110858 428940 429856 2 2017 1 1 8 5
## 5 4111495 429899 434277 2 2017 1 1 17 5
## 6 4111706 435946 436807 2 2017 1 1 12 0
## 7 4120471 443658 436768 3 2017 1 2 12 30
## 8 4120471 443658 436768 3 2017 1 2 12 30
## 9 4121054 442103 434572 2 2017 1 2 18 7
## 10 4121054 442103 434572 2 2017 1 2 18 7
## # ... with 2,193 more rows, and 12 more variables: Accidents_Date <date>,
## # Time <time>, Accidents_DateTime <dttm>, Casualty_Class <fct>,
## # Severity <fct>, Gender <fct>, Age <dbl>, Lightning_Cond <fct>,
## # Weather_Cond <fct>, Road_Class <fct>, Road_Surface <fct>,
## # Vehicle_Type <fct># Checking NAs
sum(rowSums(is.na(Accidents_2017)))## [1] 0# No NA values to exploreExploring Data Analysis
EDA1 <- Accidents_2017 %>%
group_by(Gender, Age) %>%
mutate(Count = n() ) %>%
ungroup() %>%
ggplot(mapping = aes(x=Age , y = Count)) +
geom_point(alpha = 0.6) +
facet_wrap(~Gender) +
ggtitle("Number of Casualties Per Age For Males and Females") +
ylab("Number of Casualties") +
theme_linedraw()
layout_plot <- function(my_plot, x = -0.057, y = - 0.033){
my_plot[['x']][['layout']][['annotations']][[1]][['y']] <- x
my_plot[['x']][['layout']][['annotations']][[2]][['x']] <- y
my_plot
}
ggplotly(EDA1) %>% layout_plotThe plot shows the relationship between the Number of Casualities and their Age. The graph is essential because it helps us identify which age group are more likely to be casualties. In addition, the plot is classified by the Gender, therefore; it shows how the relationship differs between males and females.
For females, as the age increases the count increases. The count peaks around the mid-20s, then the count declines gradually. The males’ graph has a similar shape as the females’. The only difference is that the males’ graph has a higher peak and the drop is sharper.
Accidents_2017 %>%
group_by(Gender, Age) %>%
summarise(Count = n() )## `summarise()` has grouped output by 'Gender'. You can override using the `.groups` argument.## # A tibble: 182 x 3
## # Groups: Gender [2]
## Gender Age Count
## <fct> <dbl> <int>
## 1 Female 1 8
## 2 Female 2 3
## 3 Female 3 6
## 4 Female 4 2
## 5 Female 5 6
## 6 Female 6 7
## 7 Female 7 8
## 8 Female 8 5
## 9 Female 9 4
## 10 Female 10 9
## # ... with 172 more rowsEDA2 <- Accidents_2017 %>%
group_by(Casualty_Class, Age) %>%
summarise(Count = n() ) %>%
ungroup() %>%
ggplot(mapping = aes(x=Age , y = Count)) +
geom_point(alpha = 0.6) +
geom_smooth()+
facet_wrap(~Casualty_Class) +
ggtitle("Count against Age based on Casualty class") +
ylab("Number of Casualties") +
theme_linedraw() ## `summarise()` has grouped output by 'Casualty_Class'. You can override using the `.groups` argument.layout_plot <- function(my_plot, x = -0.057, y = - 0.033){
my_plot[['x']][['layout']][['annotations']][[1]][['y']] <- x
my_plot[['x']][['layout']][['annotations']][[2]][['x']] <- y
my_plot
}
ggplotly(EDA2) %>% layout_plot## `geom_smooth()` using method = 'loess' and formula 'y ~ x'The plot shows the relationship between the Number of Casualities and the Age for each Casualty class. This plot is very important as it helps understand which type of casualty each age group is likely to be in a road accidents which we can use to raise awareness for different age groups separately.
When the casualty is a driver or rider, as the age increase till the mid-30s the count rockets,then the count falls rapidly. The plots for pedestrians and passengers are very similar,the only disparity is that the passengers have a higher peak. It should be highlighted that the number of casualties between the age 20 till mid-50s is awfully high when the casualty is a driver or rider compared to other casualty classes.
Accidents_2017 %>%
group_by(Casualty_Class,Age) %>%
summarise(Count = n() )## `summarise()` has grouped output by 'Casualty_Class'. You can override using the `.groups` argument.## # A tibble: 260 x 3
## # Groups: Casualty_Class [3]
## Casualty_Class Age Count
## <fct> <dbl> <int>
## 1 Driver or rider 4 1
## 2 Driver or rider 6 2
## 3 Driver or rider 7 1
## 4 Driver or rider 8 3
## 5 Driver or rider 9 1
## 6 Driver or rider 10 3
## 7 Driver or rider 11 4
## 8 Driver or rider 12 5
## 9 Driver or rider 13 5
## 10 Driver or rider 14 3
## # ... with 250 more rowsAccidents_2017 %>%
group_by(Casualty_Class) %>%
summarise(Count = n() )## # A tibble: 3 x 2
## Casualty_Class Count
## <fct> <int>
## 1 Driver or rider 1296
## 2 Pedestrian 321
## 3 Vehicle or pillion passenger 586Sections Answering Questions
Why does the number of accidents increase towards the end of the year ?
daily <- Accidents_2017 %>%
group_by(Accidents_Date) %>%
summarise(n = n())
daily## # A tibble: 360 x 2
## Accidents_Date n
## <date> <int>
## 1 2017-01-01 4
## 2 2017-01-02 7
## 3 2017-01-03 3
## 4 2017-01-04 7
## 5 2017-01-05 4
## 6 2017-01-06 5
## 7 2017-01-07 5
## 8 2017-01-09 5
## 9 2017-01-10 9
## 10 2017-01-11 7
## # ... with 350 more rowsggplot(daily, mapping = aes(Accidents_Date, n)) +
geom_line()+geom_smooth(se = FALSE)## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
# From the plot, we notice that from January till April the number of accidents per day keep decreasing. From April till around August the number of accidents per day stays constant. From August till the end of the year the number generally increases. Why is the number of accidents high at the start and end of the year?.
# Let's make a model to boarden our understanding. We will assume that number of accidents has a linear relationship with the variable Accident_Date.
mod <- lm(n ~ Accidents_Date,data = daily)
grid <- daily %>%
data_grid(Accidents_Date) %>%
add_predictions(mod)
ggplot(daily,aes(Accidents_Date,n))+
geom_line()+
geom_point(aes(y = pred),data = grid,colour = "red")
daily <- daily %>%
add_residuals(mod)
Resid_plot1 <- ggplot(daily,aes(Accidents_Date,resid))+
geom_point()+geom_ref_line(h = 0) +
geom_smooth()
ggplotly(Resid_plot1) ## `geom_smooth()` using method = 'loess' and formula 'y ~ x'# The model is not very good,it underestimates the January and fourth quarter of the year.
# Let's see the number of accidents per month and visualize it
Accidents_by_month <-
Accidents_2017 %>%
count(Month)
Accidents_by_month## # A tibble: 12 x 2
## Month n
## <dbl> <int>
## 1 1 199
## 2 2 157
## 3 3 174
## 4 4 173
## 5 5 162
## 6 6 167
## 7 7 177
## 8 8 164
## 9 9 182
## 10 10 223
## 11 11 234
## 12 12 191# Plot of Accidents per month
ggplot(data = Accidents_by_month, mapping = aes(x = Month, y = n)) +
geom_bar(aes(fill = Month) , show.legend = F, stat = "identity") +
ggtitle("Number of Accidents Per Month") +
xlab("Month") +
ylab("Number of Accidents")
# From the bar chart we understand why our model underestimates the stated months because the actual number of accidents for these months is unusually high.
# It is important to note that in Leeds, during January, October, November and December the climate is different to the rest of the year. The weather is very cloudy, the temperature drops and the number of daylight hours are low compared to the rest of the years. Could this be the reason to the high count?. Let's explore the data for these months.
Months <- Accidents_2017%>%
filter( Month %in% c(1,9,10,11,12))
Months## # A tibble: 1,029 x 21
## Reference_Number Easting Northing Vehicles_Num Year Month Day Hour Minute
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 3BE0850 430828 433222 2 2017 1 14 13 30
## 2 4110858 428940 429856 2 2017 1 1 8 5
## 3 4110858 428940 429856 2 2017 1 1 8 5
## 4 4111495 429899 434277 2 2017 1 1 17 5
## 5 4111706 435946 436807 2 2017 1 1 12 0
## 6 4120471 443658 436768 3 2017 1 2 12 30
## 7 4120471 443658 436768 3 2017 1 2 12 30
## 8 4121054 442103 434572 2 2017 1 2 18 7
## 9 4121054 442103 434572 2 2017 1 2 18 7
## 10 4121054 442103 434572 2 2017 1 2 18 7
## # ... with 1,019 more rows, and 12 more variables: Accidents_Date <date>,
## # Time <time>, Accidents_DateTime <dttm>, Casualty_Class <fct>,
## # Severity <fct>, Gender <fct>, Age <dbl>, Lightning_Cond <fct>,
## # Weather_Cond <fct>, Road_Class <fct>, Road_Surface <fct>,
## # Vehicle_Type <fct>Accidents_2017%>%
count(Lightning_Cond)## # A tibble: 5 x 2
## Lightning_Cond n
## <fct> <int>
## 1 Darkness: No street lighting 46
## 2 Darkness: Street lighting unknown 432
## 3 Darkness: Street lights present and lit 535
## 4 Darkness: Street lights present but unlit 9
## 5 Daylight: Street lights present 1181Months %>%
count(Lightning_Cond)## # A tibble: 5 x 2
## Lightning_Cond n
## <fct> <int>
## 1 Darkness: No street lighting 27
## 2 Darkness: Street lighting unknown 130
## 3 Darkness: Street lights present and lit 364
## 4 Darkness: Street lights present but unlit 2
## 5 Daylight: Street lights present 506Accidents_2017%>%
count(Road_Surface)## # A tibble: 3 x 2
## Road_Surface n
## <fct> <int>
## 1 Dry 1647
## 2 Snow 35
## 3 Wet/Damp 521Months %>%
count(Road_Surface)## # A tibble: 3 x 2
## Road_Surface n
## <fct> <int>
## 1 Dry 687
## 2 Snow 34
## 3 Wet/Damp 308Accidents_2017%>%
count(Weather_Cond)## # A tibble: 4 x 2
## Weather_Cond n
## <fct> <int>
## 1 Fine 1972
## 2 Other 21
## 3 Raining 202
## 4 Snowing 8Months %>%
count(Weather_Cond)## # A tibble: 4 x 2
## Weather_Cond n
## <fct> <int>
## 1 Fine 936
## 2 Other 11
## 3 Raining 75
## 4 Snowing 7# From our data, we see that during January, October, November and December there is a 4.4% increase in accidents in darkness, 8% increase in accidents when the road surface is wet or snow compared to the rest of the year. There was no relevant change in Weather conditions so we will ignore it for now.
# Let's try to model the relationship between road surface and lightning conditions and the count for the months of the year.
Climate <- Accidents_2017 %>%
count(Accidents_Date,Month,Road_Surface,Lightning_Cond)
mod <- lm(n ~ Road_Surface + Lightning_Cond ,data = Climate)
grid <- Climate %>%
data_grid(Month,Road_Surface,Lightning_Cond) %>%
add_predictions(mod)
ggplot(Climate,aes(Month,n))+
geom_point()+
geom_point(data = grid,aes(y = pred),colour = "red")
Climate <- Climate %>%
add_residuals(mod)
Climate## # A tibble: 953 x 6
## Accidents_Date Month Road_Surface Lightning_Cond n resid
## <date> <dbl> <fct> <fct> <int> <dbl>
## 1 2017-01-01 1 Dry Daylight: Street lights prese~ 1 -1.87
## 2 2017-01-01 1 Wet/Damp Darkness: Street lights prese~ 1 -0.721
## 3 2017-01-01 1 Wet/Damp Daylight: Street lights prese~ 2 -0.376
## 4 2017-01-02 1 Dry Darkness: No street lighting 3 0.911
## 5 2017-01-02 1 Dry Darkness: Street lights prese~ 1 -1.22
## 6 2017-01-02 1 Dry Daylight: Street lights prese~ 2 -0.875
## 7 2017-01-02 1 Wet/Damp Darkness: Street lights prese~ 1 -0.721
## 8 2017-01-03 1 Dry Darkness: Street lights prese~ 2 -0.220
## 9 2017-01-03 1 Dry Daylight: Street lights prese~ 1 -1.87
## 10 2017-01-04 1 Dry Darkness: Street lights prese~ 3 0.780
## # ... with 943 more rowsResid_plot2 <- ggplot(Climate,aes(Month,resid)) +
geom_hex()+geom_ref_line(h = 0)+geom_smooth()
ggplotly(Resid_plot2)## `geom_smooth()` using method = 'loess' and formula 'y ~ x'# Although there are some months with huge outliers the model can accurately predict for the month of January and for the fourth quarter of the year. So lets use the residuals on the Accident_Date variable to remove the pattern.
Resid_plot3 <- ggplot(Climate,aes(Accidents_Date,resid))+
geom_hex()+geom_ref_line(h = 0) +
geom_smooth()
ggplotly(Resid_plot3)## `geom_smooth()` using method = 'loess' and formula 'y ~ x'# Now we can look at the residuals, which verifies that we’ve substantially decreased the linear pattern.Through the extensive analysis that we did, we found that the number of casualties increases towards the end of the year because these months have an awful climate which makes it harder to drive. The awful Climate increases the percentage of accidents in the dark and percentage of accidents when the surface of the road is either snowy or wet which leads to higher accidents in these months. When we use a model to remove the effect caused by the climate and visualize the relationship between residuals and Accidents_dates we get a good plot. Although the residuals seem a bit biased we were able to decrease the distance between the highest and lowest residual and we got a better smooth line that has a lower confidence interval which proves we are on the right track.
Does the day of the week affect the time at which accidents happen ?
# Let's started by counting the total number of accidents for each hour and visualizing it with ggplot2
accident_hour <- Accidents_2017 %>%
count(Hour)
accident_hour## # A tibble: 24 x 2
## Hour n
## <dbl> <int>
## 1 0 30
## 2 1 23
## 3 2 9
## 4 3 15
## 5 4 16
## 6 5 12
## 7 6 41
## 8 7 85
## 9 8 143
## 10 9 105
## # ... with 14 more rowsggplot(accident_hour,aes(Hour,n))+
geom_line()+
geom_point()
# Let's try to model the relationship between hours and count.
mod1 <- lm(n ~ ns(Hour,1) ,data = accident_hour)
mod2 <- lm(n ~ ns(Hour,2) ,data = accident_hour)
mod3 <- lm(n ~ ns(Hour,3) ,data = accident_hour)
mod4 <- lm(n ~ ns(Hour,4) ,data = accident_hour)
mod5 <- lm(n ~ ns(Hour,5) ,data = accident_hour)
mod6 <- lm(n ~ ns(Hour,6) ,data = accident_hour)
grid <- accident_hour %>%
data_grid(Hour = seq_range(Hour,n = 50,expand = 0.1)) %>%
gather_predictions(mod1,mod2,mod3,mod4,mod5,mod6,.pred = "Y")
grid## # A tibble: 300 x 3
## model Hour Y
## <chr> <dbl> <dbl>
## 1 mod1 -1.15 34.6
## 2 mod1 -0.634 37.0
## 3 mod1 -0.117 39.3
## 4 mod1 0.399 41.6
## 5 mod1 0.915 44.0
## 6 mod1 1.43 46.3
## 7 mod1 1.95 48.6
## 8 mod1 2.46 51.0
## 9 mod1 2.98 53.3
## 10 mod1 3.50 55.6
## # ... with 290 more rowsggplot(accident_hour,aes(Hour,n))+
geom_point()+
geom_smooth(data = grid,aes(y = Y),colour = "red")+
facet_wrap(~ model)## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
accident_hour <- accident_hour %>%
gather_residuals(mod1,mod2,mod3,mod4,mod5,mod6)
Resid_plot4 <- ggplot(accident_hour,aes(Hour,resid)) +
geom_point()+ geom_ref_line(h = 0)+ geom_smooth()+
facet_wrap(~model)
ggplotly(Resid_plot4) %>% layout_plot## `geom_smooth()` using method = 'loess' and formula 'y ~ x'# It seems that as we increase the degrees of freedom, the better our model gets. We will stick with 6 degrees of freedom for the rest of the analysis.
# Now we will add a day of the week variable (dow) and visualize the relationship between count and hour for each day of the week.
dow_hour <- Accidents_2017 %>%
mutate(dow = wday(Accidents_DateTime,label =TRUE))%>%
count(dow,Hour)
dow_hour## # A tibble: 158 x 3
## dow Hour n
## <ord> <dbl> <int>
## 1 Sun 0 14
## 2 Sun 1 6
## 3 Sun 2 2
## 4 Sun 3 2
## 5 Sun 4 6
## 6 Sun 6 5
## 7 Sun 7 1
## 8 Sun 8 8
## 9 Sun 9 6
## 10 Sun 10 5
## # ... with 148 more rowsggplot(dow_hour,aes(Hour,n,colour = dow))+
geom_line()+
geom_point() +
labs(col = "Days of the Week")
# From the graph we notice that Sunday and Saturday have a different shape from the rest of the days. Both have a low count between 6 and 9 am compared to other days, Saturday peaks at an earlier time compared to other days. Moreover, Sunday has a lower count between 4 and 7 pm. The rest of the days have a similar shapes and follow the same trends. I think this is because the Sunday and Saturday are weekend days.
#Lets use a model to understand the relationship better.
mod <- lm(n ~ ns(Hour,6) ,data = dow_hour)
mod1 <- lm(n ~ ns(Hour,6) + dow,data = dow_hour)
mod2 <- lm(n ~ ns(Hour,6) * dow,data = dow_hour)
grid <- dow_hour %>%
data_grid(Hour = seq_range(Hour,n = 50,expand = 0.1),dow) %>%
gather_predictions(hour_alone = mod,plus_dow = mod1,multi_dow = mod2,.pred = "Y")
grid## # A tibble: 1,050 x 4
## model Hour dow Y
## <chr> <dbl> <ord> <dbl>
## 1 hour_alone -1.15 Sun 8.12
## 2 hour_alone -1.15 Mon 8.12
## 3 hour_alone -1.15 Tue 8.12
## 4 hour_alone -1.15 Wed 8.12
## 5 hour_alone -1.15 Thu 8.12
## 6 hour_alone -1.15 Fri 8.12
## 7 hour_alone -1.15 Sat 8.12
## 8 hour_alone -0.634 Sun 6.89
## 9 hour_alone -0.634 Mon 6.89
## 10 hour_alone -0.634 Tue 6.89
## # ... with 1,040 more rowsggplot(dow_hour,aes(Hour,n))+
geom_point()+
geom_smooth(data = grid,aes(y = Y),colour = "red")+
facet_wrap(~ model)## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
dow_hour <- dow_hour %>%
gather_residuals(hour_alone = mod,plus_dow = mod1,multi_dow = mod2)
Resid_plot5 <- ggplot(dow_hour,aes(Hour,resid)) +
geom_point()+ geom_ref_line(h = 0)+ geom_smooth()+
facet_wrap(~model)
ggplotly(Resid_plot5) %>% layout_plot()## `geom_smooth()` using method = 'loess' and formula 'y ~ x'# It looks like mod2 (Hour * day of the week) gives us the plot with the best residuals. Only 5 points from 168 points are outside a distance of 10 residuals.
Resid_plot6 <- dow_hour %>%
filter(model == "multi_dow") %>%
ggplot(aes(Hour,resid,colour = dow))+
geom_ref_line(h = 0) +
geom_point() +
labs(col = "Days of the Week")
ggplotly(Resid_plot6) After the broad analysis we come to the conclusion that the day of the week affects the time at which accidents happen. On workdays, we notice that most accidents happen between 6 and 9 am and between 4 and 7 pm while on weekends they can vary. When we tried to model the relationship between day of the week and the hour at which accidents happen we found that Hour multiplied by day of the week gives us the best plot.We still have a few outliners which could suggest that there is another variable that impacts the time at which accidents happen. Lastly, we found as we increase the degrees of freedom we we’re able to model the relationship between Hour and number of accidents better.